Coupling and Maximal Inequalities for Graph-Dependent Empirical Processes
图依赖经验过程的耦合与最大不等式
We develop maximal inequalities for empirical processes indexed by graph-dependent observations. Our bounds separate the complexity of the indexing class from two features specific to graph dependence: the geometry of the underlying graph and the cost of coupling graph-separated blocks to independent copies. The coupling construction combines a novel graph-adapted dependence coefficient with a coloring of a block partition. As an application, we derive Glivenko--Cantelli…